A Power of Attorney (POA) generally enables brokerages to do the things mentioned in this answer. A broker can misuse the POA in any of the following ways. Please note that I am just highlighting some possibilities here:

Pledge/Un-pledge your holdings without your knowledge. The power to do this on your behalf allows the broker to borrow money against your securities for their benefit. This can be in the form of actual loans or collateral margins for trading activities.
Store your Demat account holdings in the broker's pool or beneficiary account/s to receive corporate action benefits such as bonus shares and dividends.
Move shares from client Demats to broker account/s, to sell holdings, and buy them back at a lower price thereby profiting from the difference. Clients wouldn't get to know about such things.
Lend your shares and earn a fixed rate of return and obviously not pass it on.
Sell/use your holdings, to trade in prop book, etc. Basically, they get free access to capital and it can be risked without you finding out about it until it's too late.

There are more ways in which a broker can spin your money and securities. It is a well-known fact that POA has been severely misused by several brokerages in the past. This is not new and thus, there is a crisis of trust in the capital markets. If big names can indulge in fraudulent activities, who to trust, right? SEBI is cognizant of this and has been pushing the depositories and brokerages to implement an alternative mechanism to enable investors to buy/sell their Demat holdings without a POA. E-Delivery Instruction Slips (E-DIS) puts investors in charge of their own Demat accounts. While selling your holdings is seamless with POA, E-DIS requires you to enter OTP to verify if the transactions are authorized by the Demat account owners. Sometimes, you may not be able to sell your holdings on time using this mechanism as CDSL/NSDL portal can delay the OTP authentication process. It's new so there are teething issues but it's the future. Before you ask, let me tell you that FYERS is in the process of implementing E-DIS mechanism and we'll be live with this soon so you won't have to worry about Demat account safety. When the Karvy scandal broke out last year, I wrote a blog post highlighting the safety measures at FYERS to protect clients' interests. We are among the handful of brokerages that do not indulge in any kind of speculative activities so there is no such risk involved when dealing with us.

In what ways can a brokerage misuse Demat POA?